On a Subposet of the Tamari Lattice

We explore some of the properties of a subposet of the Tamari lattice introduced by Pallo, which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial order on the symmetric group studied by Edelman.Comment: 21 page

On absolute moments of characteristic polynomials of a certain class of complex random matrices

Integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ are obtained in terms of the characteristic polynomial of the Hermitian matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a given matrix and $U$ is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results in this context are discussed.Comment: 41 page, typos correcte

Circular Law Theorem for Random Markov Matrices

Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum. In particular, when X11 follows an exponential law, then M belongs to the Dirichlet Markov Ensemble of random stochastic matrices. Our main result states that with probability one, the counting probability measure of the complex spectrum of n^(1/2)M converges weakly as n tends to infinity to the uniform law on the centered disk of radius sigma/m. The bounded density assumption is purely technical and comes from the way we control the operator norm of the resolvent.Comment: technical update via http://HAL.archives-ouvertes.f

Alterations in regional vascular geometry produced by theoretical stent implantation influence distributions of wall shear stress: analysis of a curved coronary artery using 3D computational fluid dynamics modeling

BACKGROUND: The success of stent implantation in the restoration of blood flow through areas of vascular narrowing is limited by restenosis. Several recent studies have suggested that the local geometric environment created by a deployed stent may influence regional blood flow characteristics and alter distributions of wall shear stress (WSS) after implantation, thereby rendering specific areas of the vessel wall more susceptible to neointimal hyperplasia and restenosis. Stents are most frequently implanted in curved vessels such as the coronary arteries, but most computational studies examining blood flow patterns through stented vessels conducted to date use linear, cylindrical geometric models. It appears highly probable that restenosis occurring after stent implantation in curved arteries also occurs as a consequence of changes in fluid dynamics that are established immediately after stent implantation. METHODS: In the current investigation, we tested the hypothesis that acute changes in stent-induced regional geometry influence distributions of WSS using 3D coronary artery CFD models implanted with stents that either conformed to or caused straightening of the primary curvature of the left anterior descending coronary artery. WSS obtained at several intervals during the cardiac cycle, time averaged WSS, and WSS gradients were calculated using conventional techniques. RESULTS: Implantation of a stent that causes straightening, rather than conforms to the natural curvature of the artery causes a reduction in the radius of curvature and subsequent increase in the Dean number within the stented region. This straightening leads to modest skewing of the velocity profile at the inlet and outlet of the stented region where alterations in indices of WSS are most pronounced. For example, time-averaged WSS in the proximal portion of the stent ranged from 8.91 to 11.7 dynes/cm(2 )along the pericardial luminal surface and 4.26 to 4.88 dynes/cm(2 )along the myocardial luminal surface of curved coronary arteries as compared to 8.31 dynes/cm(2 )observed throughout the stented region of a straight vessel implanted with an equivalent stent. CONCLUSION: The current results predicting large spatial and temporal variations in WSS at specific locations in curved arterial 3D CFD simulations are consistent with clinically observed sites of restenosis. If the findings of this idealized study translate to the clinical situation, the regional geometry established immediately after stent implantation may predispose portions of the stented vessel to a higher risk of neointimal hyperplasia and subsequent restenosis

Neurobiological degeneracy and affordance perception support functional intra-individual variability of inter-limb coordination during ice climbing

This study investigated the functional intra-individual movement variability of ice climbers differing in skill level to understand how icefall properties were used by participants as affordances to adapt inter-limb coordination patterns during performance. Seven expert climbers and seven beginners were observed as they climbed a 30 m icefall. Movement and positioning of the left and right hand ice tools, crampons and the climber's pelvis over the first 20 m of the climb were recorded and digitized using video footage from a camera (25 Hz) located perpendicular to the plane of the icefall. Inter-limb coordination, frequency and types of action and vertical axis pelvis displacement exhibited by each climber were analysed for the first five minutes of ascent. Participant perception of climbing affordances was assessed through: (i) calculating the ratio between exploratory movements and performed actions, and (ii), identifying, by self-confrontation interviews, the perceptual variables of environmental properties, which were significant to climbers for their actions. Data revealed that experts used a wider range of upper and lower limb coordination patterns, resulting in the emergence of different types of action and fewer exploratory movements, suggesting that effective holes in the icefall provided affordances to regulate performance. In contrast, beginners displayed lower levels of functional intra-individual variability of motor organization, due to repetitive swinging of ice tools and kicking of crampons to achieve and maintain a deep anchorage, suggesting lack of perceptual attunement and calibration to environmental properties to support climbing performanc

Cultural Diversity and Saccade Similarities: Culture Does Not Explain Saccade Latency Differences between Chinese and Caucasian Participants

A central claim of cultural neuroscience is that the culture to which an individual belongs plays a key role in shaping basic cognitive processes and behaviours, including eye movement behaviour. We previously reported a robust difference in saccade behaviour between Chinese and Caucasian participants; Chinese participants are much more likely to execute low latency express saccades, in circumstances in which these are normally discouraged. To assess the extent to which this is the product of culture we compared a group of 70 Chinese overseas students (whose primary cultural exposure was that of mainland China), a group of 45 participants whose parents were Chinese but who themselves were brought up in the UK (whose primary cultural exposure was western European) and a group of 70 Caucasian participants. Results from the Schwartz Value Survey confirmed that the UK-Chinese group were culturally similar to the Caucasian group. However, their patterns of saccade latency were identical to the mainland Chinese group, and different to the Caucasian group. We conclude that at least for the relatively simple reflexive saccade behaviour we have investigated, culture cannot explain the observed differences in behaviour

Analysis of In-Vivo LacR-Mediated Gene Repression Based on the Mechanics of DNA Looping

Interactions of E. coli lac repressor (LacR) with a pair of operator sites on the same DNA molecule can lead to the formation of looped nucleoprotein complexes both in vitro and in vivo. As a major paradigm for loop-mediated gene regulation, parameters such as operator affinity and spacing, repressor concentration, and DNA bending induced by specific or non-specific DNA-binding proteins (e.g., HU), have been examined extensively. However, a complete and rigorous model that integrates all of these aspects in a systematic and quantitative treatment of experimental data has not been available. Applying our recent statistical-mechanical theory for DNA looping, we calculated repression as a function of operator spacing (58–156 bp) from first principles and obtained excellent agreement with independent sets of in-vivo data. The results suggest that a linear extended, as opposed to a closed v-shaped, LacR conformation is the dominant form of the tetramer in vivo. Moreover, loop-mediated repression in wild-type E. coli strains is facilitated by decreased DNA rigidity and high levels of flexibility in the LacR tetramer. In contrast, repression data for strains lacking HU gave a near-normal value of the DNA persistence length. These findings underscore the importance of both protein conformation and elasticity in the formation of small DNA loops widely observed in vivo, and demonstrate the utility of quantitatively analyzing gene regulation based on the mechanics of nucleoprotein complexes

A competitive integration model of exogenous and endogenous eye movements

We present a model of the eye movement system in which the programming of an eye movement is the result of the competitive integration of information in the superior colliculi (SC). This brain area receives input from occipital cortex, the frontal eye fields, and the dorsolateral prefrontal cortex, on the basis of which it computes the location of the next saccadic target. Two critical assumptions in the model are that cortical inputs are not only excitatory, but can also inhibit saccades to specific locations, and that the SC continue to influence the trajectory of a saccade while it is being executed. With these assumptions, we account for many neurophysiological and behavioral findings from eye movement research. Interactions within the saccade map are shown to account for effects of distractors on saccadic reaction time (SRT) and saccade trajectory, including the global effect and oculomotor capture. In addition, the model accounts for express saccades, the gap effect, saccadic reaction times for antisaccades, and recorded responses from neurons in the SC and frontal eye fields in these tasks. © The Author(s) 2010